Centrifugal-pendulum vibration absorbing device and order setting method for the same

ABSTRACT

A centrifugal-pendulum vibration absorbing device comprising having a support member coupled to a rotary element that is rotated by power from a drive device, and a mass body coupled to the support member so as to swing about a pendulum fulcrum and rotate about a center of gravity. An order of vibration of the mass body is determined on the basis of an order of vibration to be damped generated by the drive device in consideration of at least a rotational angle of the mass body about the pendulum fulcrum and a rotational angle of the mass body about the center of gravity.

INCORPORATION BY REFERENCE

The disclosure of Japanese Patent Application No. 2012-282756 filed onDec. 26, 2012 including the specification, drawings and abstract andU.S. Provisional Application No. 61/746,009 filed Dec. 26, 2012 areincorporated herein by reference in their entirety.

BACKGROUND OF THE INVENTION

The present invention relates to a centrifugal-pendulum vibrationabsorbing device including a support member coupled to a rotary elementthat is rotated by power from a drive device and a mass body supportedby the support member so as to be swingable, and to an order settingmethod for the centrifugal-pendulum vibration absorbing device.

DESCRIPTION OF THE RELATED ART

Hitherto, there has been known a centrifugal-pendulum vibrationabsorbing device including a mass body (a pendulum mass) coupled to adisc member (a support member) so as to swing about a pendulum fulcrumand rotate about a center of gravity (see German Patent ApplicationPublication No. 10 2011 085 983 A1, for example). In thecentrifugal-pendulum vibration absorbing device, the rotational angle(108) of the mass body is equal to the angle of deviation (104) at anypoint on a pendulum track.

SUMMARY OF THE INVENTION

In order to improve the vibration absorbing performance of thecentrifugal-pendulum vibration absorbing device discussed above, it isnecessary to adequately set the order of vibration of the mass body onthe basis of the order of vibration to be damped by thecentrifugal-pendulum vibration absorbing device. However, German PatentApplication Publication No. 10 2011 085 983 A1 mentioned above does notdescribe at all setting the order of vibration of the mass body providedin the centrifugal-pendulum vibration absorbing device and coupled tothe support member so as to swing about the pendulum fulcrum and rotateabout the center of gravity.

It is therefore a main object of the present invention to improve thevibration absorbing performance by adequately setting the order ofvibration of a mass body provided in a centrifugal-pendulum vibrationabsorbing device and coupled to a support member so as to swing about apendulum fulcrum and rotate about a center of gravity.

In order to achieve the foregoing main object, the centrifugal-pendulumvibration absorbing device and the order setting method for thecentrifugal-pendulum vibration absorbing device according to the presentinvention adopt the following means.

A first aspect of the present invention provides a centrifugal-pendulumvibration absorbing device including: a support member coupled to arotary element that is rotated by power from a drive device; and a massbody coupled to the support member so as to swing about a pendulumfulcrum and rotate about a center of gravity. In thecentrifugal-pendulum vibration absorbing device, an order of vibrationof the mass body is determined on the basis of an order of vibrationgenerated by the drive device in consideration of at least a rotationalangle of the mass body about the pendulum fulcrum and a rotational angleof the mass body about the center of gravity.

The inventors conducted diligent studies on setting the order ofvibration of a mass body provided in a centrifugal-pendulum vibrationabsorbing device and coupled to a support member so as to swing about apendulum fulcrum and rotate about a center of gravity. As a result, theinventors found that motion of the mass body provided in this type ofcentrifugal-pendulum vibration absorbing device may be treated as motionof a mass body provided in a so-called roller centrifugal-pendulumvibration absorbing device, in which a roller serving as the mass bodyswings about a pendulum fulcrum and rotates about a center of gravity,irrespective of the form (structure).

That is, in the roller centrifugal-pendulum vibration absorbing device,the roller serving as the mass body rolls on a curved guide surfacewhile rotating about the center of gravity (an axis). In the light ofthis, the inventors divided motion of the roller in the rollercentrifugal-pendulum vibration absorbing device into translationalmotion (sliding motion) along the guide surface not involving rotationof the roller about the center of gravity and rotational motion of theroller about the center of gravity, and treated motion of the roller asthe total of swing motion of the roller about the pendulum fulcrumwithout rotation about the center of gravity and rotational motion ofthe roller about the center of gravity.

Here, it is known that the order of vibration of a mass body provided ina centrifugal-pendulum vibration absorbing device so as to swing about apendulum fulcrum without rotating about a center of gravity isconveniently represented as follows:√(distance from rotational center to pendulum fulcrum/distance frompendulum fulcrum to center of gravity of mass body)  (A)In contrast, it is known that the order of vibration of a rollerprovided in a roller centrifugal-pendulum vibration absorbing device isconveniently represented as follows:√(2×distance from rotational center to pendulum fulcrum/3×distance frompendulum fulcrum to center of gravity of roller)  (B)In the studies, the inventors focused on the difference (a decrease)between the order of vibration of (B) given above and the order ofvibration of (A) given above. Because swing motion of the mass bodyabout the pendulum fulcrum corresponds to translational motion of theroller along the guide surface, the inventors estimated that thedifference between the order of vibration of (B) and the order ofvibration of (A) was caused by rotational motion of the roller about thecenter of gravity, specifically, the moment of inertia due to rotationof the roller about the center of gravity which was proportional to thesquare of the ratio between the radius of the roller and the distancefrom the pendulum fulcrum to the center of gravity of the roller. Then,through verifications performed by analyses or the like, the inventorsconfirmed that such an estimation was extremely adequate, and thatmotion of the mass body provided in the centrifugal-pendulum vibrationabsorbing device and coupled to the support member so as to swing aboutthe pendulum fulcrum and rotate about the center of gravity might betreated as the total of swing motion of the mass body about the pendulumfulcrum without rotation about the center of gravity and rotationalmotion of the mass body about the center of gravity.

Meanwhile, a distance d1 along the guide surface from a point oftangency between the guide surface and the roller with the roller (themass body) stationary at the swing center to a point of tangency betweenthe guide surface and the roller with the roller swung to one side inthe swing range is represented by the sum of the distance from thependulum fulcrum to the center of gravity of the roller and the radiusof the roller and the rotational angle of the roller (the center ofgravity) about the pendulum fulcrum. In addition, a distance d2 alongthe outer peripheral surface of the roller from a point of tangencybetween the guide surface and the roller with the roller stationary atthe swing center to a point of tangency between the guide surface andthe roller with the roller swung to one side in the swing range isrepresented by the sum of the rotational angle of the roller about thependulum fulcrum and the rotational angle of the roller about the centerof gravity due to translation and rotation of the roller about thecenter of gravity and the radius of the roller. If the roller rolls onthe guide surface without slipping, the distance d1 and the distance d2coincide with each other. By utilizing this relationship, the ratiobetween the radius of the roller and the distance from the pendulumfulcrum to the center of gravity of the roller can be replaced with theratio between the rotational angle of the roller about the pendulumfulcrum and the rotational angle of the roller about the center ofgravity. Consequently, the moment of inertia due to rotation of theroller about the center of gravity can be represented using the ratiobetween the rotational angle of the roller about the pendulum fulcrumand the rotational angle of the roller about the center of gravity.

Thus, the order of vibration of the mass body provided in thecentrifugal-pendulum vibration absorbing device and coupled to thesupport member so as to swing about the pendulum fulcrum and rotateabout the center of gravity can be determined on the basis of the orderof vibration of the mass body which swings about the pendulum fulcrumwithout rotation about the center of gravity and further inconsideration of rotational motion of the mass body about the center ofgravity (the moment of inertia due to rotation), that is, the rotationalangle of the mass body about the pendulum fulcrum and the rotationalangle of the mass body about the center of gravity. Then, it is possibleto improve the vibration absorbing performance by adequately setting theorder of vibration of the mass body in the centrifugal-pendulumvibration absorbing device by determining the order of vibration of themass body on the basis of the order of vibration generated by the drivedevice in consideration of at least the rotational angle of the massbody about the pendulum fulcrum and the rotational angle of the massbody about the center of gravity.

The order of vibration of the mass body may be determined on the basisof the order of vibration to be damped from a distance from a rotationalcenter of the rotary element to the pendulum fulcrum, a distance fromthe pendulum fulcrum to the center of gravity of the mass body, a massof the mass body, and a product of a square of a ratio between therotational angle of the mass body about the pendulum fulcrum and therotational angle of the mass body about the center of gravity and amoment of inertia of the mass body.

The support member and the mass body may be disposed within a liquidchamber that stores a liquid, and the order of vibration may bedetermined further in consideration of a force caused by a centrifugalliquid pressure generated within the liquid chamber along with rotationof the rotary element to act on the mass body. That is, according to thestudies conducted by the inventors, it was revealed that in thecentrifugal-pendulum vibration absorbing device disposed within theliquid chamber which stores the liquid, swing motion of the mass body inthe presence of the liquid was significantly affected by a force due tothe centrifugal liquid pressure generated within the liquid chamberalong with rotation of the rotary element. Thus, for thecentrifugal-pendulum vibration absorbing device disposed within theliquid chamber which stores the liquid, it is possible to improve thevibration absorbing performance by adequately setting the order ofvibration of the mass body by determining the order of vibration of themass body further in consideration of the force caused by thecentrifugal liquid pressure generated within the liquid chamber alongwith rotation of the rotary element to act on the mass body.

In a (dry) centrifugal-pendulum vibration absorbing device which is notdisposed within the liquid chamber which stores the liquid, when theorder of vibration is defined as “n”, the mass of the mass body isdefined as “m”, the distance from the rotational center to the pendulumfulcrum is defined as “R”, the distance from the pendulum fulcrum to thecenter of gravity of the mass body is defined as “r”, the rotationalangle of the mass body about the pendulum fulcrum is defined as “φ”, therotational angle of the mass body about the center of gravity is definedas “θ”, and the moment of inertia of the mass body is defined as “I”,

the order of vibration n may be determined using the followingrelational formula:n=√{m·R·r/[m· ² +I·(θ/φ)²]}

Consequently, the order of vibration of the mass body in thecentrifugal-pendulum vibration absorbing device which is not disposedwithin the liquid chamber which stores the liquid can be made adequatein consideration of the force caused by the centrifugal liquid pressuregenerated within the liquid chamber along with rotation of the rotaryelement to act on the mass body.

In a (wet) centrifugal-pendulum vibration absorbing device disposedwithin a liquid chamber which stores a liquid, when the order ofvibration is defined as “n”, the mass of the mass body is defined as“m”, the distance from the rotational center to the pendulum fulcrum isdefined as “R”, the distance from the pendulum fulcrum to the center ofgravity of the mass body is defined as “r”, the rotational angle of themass body about the pendulum fulcrum is defined as “φ”, the rotationalangle of the mass body about the center of gravity is defined as “θ”,the moment of inertia of the mass body is defined as “I”, and a valueobtained by dividing the force caused by the centrifugal liquid pressureto act on the mass body by a square of a rotational angular speed of therotary element and further dividing the resulting quotient by a productof the mass and the distance from the pendulum fulcrum to the center ofgravity of the mass body is defined as “α”,

the order of vibration n may be determined using the followingrelational formula:n=√{m·r ²·(R/r−α)/[m·r ² +I·(θ/φ)²]}

Consequently, the order of vibration of the mass body in thecentrifugal-pendulum vibration absorbing device disposed within theliquid chamber which stores the liquid can be made adequate inconsideration of the force caused by the centrifugal liquid pressuregenerated within the liquid chamber along with rotation of the rotaryelement to act on the mass body.

When the order of vibration to be damped is defined as “Ntag”, thecentrifugal-pendulum vibration absorbing device including the mass bodycoupled to the support member so as to swing about the pendulum fulcrumand rotate about the center of gravity may be designed to meet thefollowing relational formula:Ntag−0.2≦n≦Ntag+0.2More preferably, the centrifugal-pendulum vibration absorbing device maybe designed to meet the following relational formula:Ntag−0.1≦n≦Ntag+0.1This makes it possible to adequately set the order of vibration of themass body also in consideration of the effect of the manufacturingtolerance or the like.

A second aspect of the present invention provides an order settingmethod for a centrifugal-pendulum vibration absorbing device including asupport member coupled to a rotary element that is rotated by power froma drive device and a mass body coupled to the support member so as toswing about a pendulum fulcrum and rotate about a center of gravity. Themethod includes determining an order of vibration of the mass body onthe basis of an order of vibration generated by the drive device inconsideration of at least a rotational angle of the mass body about thependulum fulcrum and a rotational angle of the mass body about thecenter of gravity.

According to the method, it is possible to improve the vibrationabsorbing performance of the centrifugal-pendulum vibration absorbingdevice including the mass body coupled to the support member so as toswing about the pendulum fulcrum and rotate about the center of gravityby adequately setting the order of vibration of the mass body.

The order of vibration of the mass body may be determined on the basisof the order of vibration to be damped from a distance from a rotationalcenter of the rotary element to the pendulum fulcrum, a distance fromthe pendulum fulcrum to the center of gravity of the mass body, a massof the mass body, and a product of a square of a ratio between therotational angle of the mass body about the pendulum fulcrum and therotational angle of the mass body about the center of gravity and amoment of inertia of the mass body.

The support member and the mass body may be disposed within a liquidchamber that stores a liquid, and the order of vibration may bedetermined further in consideration of a force caused by a centrifugalliquid pressure generated within the liquid chamber along with rotationof the rotary element to act on the mass body.

In a (dry) centrifugal-pendulum vibration absorbing device which is notdisposed within the liquid chamber which stores the liquid, when theorder of vibration is defined as “n”, the mass of the mass body isdefined as “m”, the distance from the rotational center to the pendulumfulcrum is defined as “R”, the distance from the pendulum fulcrum to thecenter of gravity of the mass body is defined as “r”, the rotationalangle of the mass body about the pendulum fulcrum is defined as “φ”, therotational angle of the mass body about the center of gravity is definedas “θ”, and the moment of inertia of the mass body is defined as “I”,

the order of vibration n may be determined using the followingrelational formula:n−√{m·R·r/[m·r ² +I·(θφ)²]}

In a (wet) centrifugal-pendulum vibration absorbing device disposedwithin a liquid chamber which stores a liquid, when the order ofvibration is defined as “n”, the mass of the mass body is defined as“m”, the distance from the rotational center to the pendulum fulcrum isdefined as “R”, the distance from the pendulum fulcrum to the center ofgravity of the mass body is defined as “r”, the rotational angle of themass body about the pendulum fulcrum is defined as “φ”, the rotationalangle of the mass body about the center of gravity is defined as “θ”,the moment of inertia of the mass body is defined as “I”, and a valueobtained by dividing the force caused by the centrifugal liquid pressureto act on the mass body by a square of a rotational angular speed of therotary element and further dividing the resulting quotient by a productof the mass and the distance from the pendulum fulcrum to the center ofgravity of the mass body is defined as “α”,

the order of vibration n may be determined using the followingrelational formula:n=√{m·r ²·(R/r−α)/[m·r ² +I·(θ/φ)²]}

When the order of vibration to be damped is defined as “Ntag”, thecentrifugal-pendulum vibration absorbing device may be designed to meetthe following relational formula:Ntag−0.2≦n≦Ntag+0.2More preferably, the centrifugal-pendulum vibration absorbing device maybe designed to meet the following relational formula:Ntag−0.1≦n=√[(R/r−α]≦Ntag+0.1

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating the configuration of astarting device including a centrifugal-pendulum vibration absorbingdevice according to an embodiment of the present invention;

FIG. 2 is a schematic diagram illustrating the configuration of thecentrifugal-pendulum vibration absorbing device according to theembodiment of the present invention;

FIG. 3 illustrates a method of setting the order of vibration of a massbody forming the centrifugal-pendulum vibration absorbing device; and

FIG. 4 illustrates the method of setting the order of vibration of themass body forming the centrifugal-pendulum vibration absorbing device.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Now, an embodiment of the present invention will be described withreference to the drawings.

FIG. 1 is a schematic diagram illustrating the configuration of astarting device 1 including a centrifugal-pendulum vibration absorbingdevice 10 according to an embodiment of the present invention. Thestarting device 1 illustrated in the drawing is mounted on a vehicleincluding an engine (an internal combustion engine) serving as a motor,and transmits power from the engine to a transmission that is anautomatic transmission (AT) or a continuously variable transmission(CVT). In addition to the centrifugal-pendulum vibration absorbingdevice 10, the starting device 1 includes a front cover (an inputmember) 3 coupled to a crankshaft of the engine, a pump impeller (aninput-side fluid transmission element) 4 fixed to the front cover 3, aturbine runner (an output-side fluid transmission element) 5 disposedcoaxially with the pump impeller 4 so as to be rotatable, a stator 6that rectifies a flow of working oil (a working fluid) from the turbinerunner 5 to the pump impeller 4, a damper hub (an output member) 7 fixedto an input shaft IS of the transmission, a damper mechanism 8 connectedto the damper hub 7, and a single-plate friction lock-up clutch 9including a lock-up piston (not illustrated) connected to the dampermechanism 8.

The pump impeller 4 and the turbine runner 5 face each other. The stator6 is disposed between and coaxially with the pump impeller 4 and theturbine runner 5 so as to be rotatable. The rotational direction of thestator 6 is set to only one direction by a one-way clutch 60. The pumpimpeller 4, the turbine runner 5, and the stator 6 form a torus (anannular flow passage) that allows circulation of the working oil (afluid) inside a fluid transmission chamber (a liquid chamber) 2 definedby the front cover 3 and a pump shell of the pump impeller 4, andfunctions as a torque converter having a torque amplifying function. Inthe starting device 1, the stator 6 and the one-way clutch 60 may beomitted, and the pump impeller 4 and the turbine runner 5 may functionas a fluid coupling.

The damper mechanism 8 includes a drive member 81 serving as an inputelement capable of rotating together with the lock-up piston of thelock-up clutch 9, a plurality of first coil springs (first elasticbodies) SP1, an intermediate member (an intermediate element) 82 engagedwith the drive member 81 via the first coil springs SP1, a plurality ofsecond coil springs (second elastic bodies) SP2 having rigidity (aspring constant) that is higher than that of the first coil springs SP1and disposed apart from the first coil springs SP1 in the radialdirection of the starting device 1, for example, and a driven member (anoutput element) 83 engaged with the intermediate member 82 via thesecond coil springs SP2.

The drive member 81 includes a plurality of abutment portions that abutagainst respective first ends of the corresponding first coil springsSP1, and holds the plurality of first coil springs SP1. The intermediatemember 82 includes a plurality of abutment portions that abut againstrespective second ends of the corresponding first coil springs SP1, anda plurality of abutment portions that abut against respective first endsof the corresponding second coil springs SP2. The driven member 83includes a plurality of abutment portions that abut against respectivesecond ends of the corresponding second coil springs SP2, and is fixedto the damper hub 7. In the starting device 1 according to theembodiment, in addition, the intermediate member 82 of the dampermechanism 8, which tends to vibrate between the first and second coilsprings SP1 and SP2, is coupled to the turbine runner 5 via a pluralityof third coil springs (third elastic bodies) SP3. The plurality of thirdcoil springs SP3 and the turbine runner 5 form a dynamic damper 20. Thisenables both the centrifugal-pendulum vibration absorbing device 10 andthe dynamic damper 20 to favorably absorb vibration of the intermediatemember 82 and vibration of the entire damper mechanism 8 duringengagement of the lock-up clutch 9 (during lock-up).

The lock-up clutch 9 operates on a hydraulic pressure from a hydrauliccontrol device (not illustrated). The lock-up clutch 9 establishes andreleases lock-up in which the front cover (an input member) 3 and thedamper hub 7, that is, the input shaft IS of the transmission, arecoupled to each other via the damper mechanism 8. The lock-up piston(not illustrated) forming the lock-up clutch 9 is supported by thedamper hub 7 so as to be movable in the axial direction and rotatable,for example. An annular friction material is affixed to a surface of thelock-up piston on the outer peripheral side and on the side of the frontcover 3. The drive member 81 discussed above is coupled to the outerperipheral portion of the lock-up piston. The starting device 1 may beconfigured to include a multi-plate friction lock-up clutch in place ofthe single-plate friction lock-up clutch 9.

As illustrated in FIG. 1, the centrifugal-pendulum vibration absorbingdevice 10 includes a support member (a flange) 11 coaxially attached tothe driven member 83 serving as a rotary element of the damper mechanism8, and a plurality of (for example, three to four) mass bodies 12 thatare supported by the support member 11 so as to be swingable and thatare adjacent to each other in the circumferential direction. Thecentrifugal-pendulum vibration absorbing device 10 is disposed insidethe fluid transmission chamber 2 (a liquid chamber) defined by the frontcover 3 and the pump shell of the pump impeller 4 to store the workingoil. The centrifugal-pendulum vibration absorbing device 10 absorbs(damps) vibration between the front cover 3 and the damper hub 7 withthe plurality of mass bodies 12 swung in the same direction with respectto the support member 11 inside the fluid transmission chamber 2 filledwith the working oil along with rotation of the support member 11 toapply to the driven member 83 of the damper mechanism 8 vibration thatis opposite in phase to vibration (resonance) of the driven member 83.

In the embodiment, two (a pair of) first guide notch portions (notillustrated) are formed in the support member 11 for each of the massbodies 12, and two (a pair of) second guide notch portions (notillustrated) are formed in each of the mass bodies 12. The supportmember 11 and each of the mass bodies 12 are coupled to each other via aguide roller formed by integrating a first roller that rolls on theinner peripheral surfaces of the first guide notch portions of thesupport member 11 and a second roller that rolls on the inner peripheralsurfaces of the second guide notch portions of each of the mass bodies12 (all not illustrated). The pair of first guide notch portions of thesupport member 11 corresponding to each of the mass bodies 12 are formedas long holes that are horizontally asymmetrical or horizontallysymmetrical with respect to each other and that each extend with a curvethat is convex toward the radially outer side of the support member 11as their axis, for example, and disposed symmetrically with respect tothe swing center line of the mass body 12 (a line including therotational center (an axis) of the driven member 83 (the support member11) and a pendulum fulcrum PF). In contrast, the pair of second guidenotch portions of each of the mass bodies 12 are formed as long holesthat are horizontally asymmetrical or horizontally symmetrical withrespect to each other and that each extend with a curve that is convextoward the center of the support member 11 as their axis, for example,and disposed symmetrically with respect to the swing center line of themass body 12.

Consequently, in the centrifugal-pendulum vibration absorbing device 10according to the embodiment, the guide roller described above is guidedby both the first guide notch portions of the support member 11 and thesecond guide notch portions of the mass bodies 12, which allows each ofthe mass bodies 12 to turn about the pendulum fulcrum PF and rotateabout a center of gravity G of the mass body 12 as the mass body 12 isswung within the swing range as illustrated in FIG. 2 along withrotation of the support member 11. As a result, it is possible to dampvibration to be transmitted to the support member 11 by utilizing notonly swing motion of the mass bodies 12 about the pendulum fulcrum PFbut also the moment of rotation of the mass bodies 12 about the centerof gravity G. One first guide notch portion may be formed in the supportmember 11 for each of the mass bodies 12, and one second guide notchportion may be formed in each of the mass bodies 12. Thecentrifugal-pendulum vibration absorbing device may be formed as aso-called bifilar device that includes as the support member 11 two armmembers that support one mass body so as to be swingable.

Next, a method of setting the order of vibration of the mass body 12 inthe centrifugal-pendulum vibration absorbing device 10 will be describedwith reference to FIGS. 2 to 4.

With regard to the centrifugal-pendulum vibration absorbing devicedisposed inside the liquid chamber such as the fluid transmissionchamber 2 which stores the working oil as discussed above, the inventorsfirst conducted diligent studies on the effect of the liquid such as theworking oil on motion of the mass body. Then, as a result of conductingvarious analyses, it was revealed that in this type ofcentrifugal-pendulum vibration absorbing device, the effect of a viscousdrag on swing motion of the mass body in the presence of the liquid suchas the working oil was extremely small, and the swing motion of the massbody in the presence of the liquid was significantly affected by a forcedue to a centrifugal liquid pressure (a centrifugal hydraulic pressure)generated within the liquid chamber such as the fluid transmissionchamber 2 along with rotation of the rotary element such as the drivenmember 83 which is rotated by power from the engine.

Here, a consideration is made on a force due to a centrifugal liquidpressure that acts on an arcuate mass body 12 x such as that illustratedin FIG. 3 when the mass body 12 x swings about the pendulum fulcrum PFwithout rotating about the center of gravity along with rotation of therotary element such as the driven member 83. The mass body 12 xillustrated in FIG. 3 has an outer peripheral surface in the shape of acylindrical surface centered on a rotational center RC of the rotaryelement (the support member), an inner peripheral surface in the shapeof a concave cylindrical surface centered on the rotational center RC,and two side surfaces that are parallel to the swing center line (seethe dash-dotted line in the drawing), and has a uniform thickness. Whenthe distance (radius of curvature) from the rotational center RC to theouter peripheral surface of the mass body 12 x is defined as “Ro”, thedistance (radius of curvature) from the rotational center RC to theinner peripheral surface of the mass body 12 x is defined as “Ri”, thethickness of the mass body 12 x is defined as “t”, the length from theswing center line to the left and right end portions of the mass body 12x is defined as “L”, the rotational angular speed of the rotary elementis defined as “ω”, and the density of the liquid such as the working oilis defined as “ρ”, a force Fp due to the centrifugal liquid pressurethat acts on the mass body 12 x is represented by the following formula(1):Fp=ρ·ω ² ·t·L·(Ro ² −Ri ²)  [Formula 1]

When the rotary element such as the driven member 83 rotates, acentrifugal force Fc acts on the mass body 12 x. Thus, when the mass ofthe mass body 12 x is defined as “m”, the distance from the rotationalcenter RC to the pendulum fulcrum PF is defined as “R”, and the distancefrom the pendulum fulcrum PF to the center of gravity G of the mass body12 x is defined as “r”, a force F that acts on the mass body 12 x whenthe mass body 12 x swings about the pendulum fulcrum PF along withrotation of the rotary element is represented by the following formula(2). Then, if a dimensionless value obtained by dividing the force Fpdue to the centrifugal liquid pressure which acts on the mass body 12 xby the square of the rotational angular speed w and further dividing theresulting quotient by the product of the mass m and the distance r isdefined as “α” as represented by the following formula (3), the force Fwhich acts on the mass body 12 x is represented by the following formula(4):

$\begin{matrix}\lbrack {{Formula}\mspace{14mu} 2} \rbrack & \; \\\begin{matrix}{F = {{Fc} + {Fp}}} \\{= {{m \cdot R \cdot \omega^{2}} - {\rho \cdot \omega^{2} \cdot t \cdot L \cdot ( {{R\; o^{2}} - {Ri}^{2}} )}}} \\{= {m \cdot r \cdot \omega^{2} \cdot \lbrack {\frac{R}{r} - \frac{\rho \cdot t \cdot L \cdot ( {{Ro}^{2} - {Ri}^{2}} )}{m \cdot r}} \rbrack}}\end{matrix} & (2) \\{\alpha = \frac{\rho \cdot t \cdot L \cdot ( {{R\; o^{2}} - {Ri}^{2}} )}{m \cdot r}} & (3) \\{F = {m \cdot r \cdot \omega^{2} \cdot ( {\frac{R}{r} - \alpha} )}} & (4)\end{matrix}$

Further, when the rotational angle of the mass body 12 x about thependulum fulcrum PF during swing about the pendulum fulcrum PF alongwith rotation of the rotary element is defined as “φ”, the equation ofmotion of the centrifugal-pendulum vibration absorbing device includingthe mass body 12 x is represented by the following formula (5). Itshould be noted that the term on the right side of the formula (5) is aviscous term indicating the effect of a viscous drag due to relativemotion between the mass body and the rotating liquid (working oil), andthat “c” is a constant. The viscous term of the formula (5) can berepresented by the following formula (6) by introducing an appropriatemodel into the viscous term. The formula (5) can be modified into thefollowing formula (7) using the relationship of the formula (6). Itshould be noted that in the formula (6), “μ” is a viscosity coefficient,“k” is a coefficient determined on the basis of the viscosity of theliquid and the frequency of swing motion of the mass body, and “A” isthe surface area of the mass body 12 x.

$\begin{matrix}\lbrack {{Formula}\mspace{14mu} 3} \rbrack & \; \\{{{m \cdot r \cdot \overset{¨}{\phi}} + {m \cdot r \cdot \omega^{2} \cdot ( {\frac{R}{r} - \alpha} ) \cdot \phi}} = {{- c} \cdot \overset{.}{\phi}}} & (5) \\{{c \cdot \overset{.}{\phi}} = {{- \mu} \cdot k \cdot A \cdot ( {R - r} ) \cdot \overset{.}{\phi}}} & (6) \\{{\overset{¨}{\phi} + {\frac{\mu \cdot k \cdot A \cdot ( {R + r} )}{m \cdot r} \cdot \overset{.}{\phi}} + {{\omega^{2}( {\frac{R}{r} - \alpha} )} \cdot \phi}} = 0} & (7)\end{matrix}$

The following formula (8) which indicates an order of vibration n_(x) ofthe mass body 12 x which swings about the pendulum fulcrum PF withoutrotating about the center of gravity in the presence of the liquid canbe obtained by introducing a dimensionless value “β” indicating theviscous term into the natural vibration frequency of the mass body 12 xobtained from the formula (7). It should be noted, however, that theeffect of a viscous drag on swing motion of the mass body in thepresence of the liquid such as the working oil is extremely small asdiscussed above. Thus, “β” in the formula (8) can be ignored, and thusthe order of vibration n_(x) of the mass body 12 x which swings aboutthe pendulum fulcrum PF without rotating about the center of gravity inthe presence of the liquid can be represented by the following formula(9):

$\begin{matrix}\lbrack {{Formula}\mspace{14mu} 4} \rbrack & \; \\{n_{x} = \sqrt{\frac{R}{r} - \alpha - \beta}} & (8) \\{n_{x} = \sqrt{\frac{R}{r} - \alpha}} & (9)\end{matrix}$

In obtaining the value α by dividing the force Fp due to the centrifugalliquid pressure which acts on the mass body by the square of therotational angular speed ω and further dividing the resulting quotientby the product of the mass m and the distance R, in the case where theshape of the mass is relatively simple as with the mass body 12 xdiscussed above, the force Fp caused by the centrifugal liquid pressureto act on the mass body can be obtained easily and accurately bydetermining the force Fp using the density ρ of the liquid and thedifference in area between the outer peripheral surface and the innerperipheral surface of the mass body. In the case where the shape of themass body is complicated, the force Fp may be calculated by performingnumerical calculation in consideration of the shape of the mass body 12.

In addition to the effect of the liquid such as the working oil onmotion of the mass body discussed above, the inventors also conducteddiligent studies on setting the order of vibration of a mass bodyprovided in a centrifugal-pendulum vibration absorbing device andcoupled to a support member so as to swing about a pendulum fulcrum androtate about a center of gravity. Then, as a result of various analysesconducted with a focus on a so-called roller centrifugal-pendulumvibration absorbing device in the course of the studies, the inventorsfound that motion of a mass body in this type of centrifugal-pendulumvibration absorbing device may be treated as motion of a mass body inthe so-called roller centrifugal-pendulum vibration absorbing deviceirrespective of the form (structure).

As illustrated in FIG. 4, the roller centrifugal-pendulum vibrationabsorbing device includes a guide notch portion 110 (in the example ofFIG. 4, a circular opening) formed in a member corresponding to thesupport member 11 of the centrifugal-pendulum vibration absorbing device10 described above, and a roller 120 that rolls on a guide surface 111that is the inner peripheral surface (in the example of FIG. 4, aconcave circumferential surface) of the guide notch portion 110. In theroller centrifugal-pendulum vibration absorbing device illustrated inFIG. 4, the roller 120 serving as the mass body rolls on the curvedguide surface 111 while rotating about the center of gravity G (anaxis). In the light of this, the inventors divided motion of the rollerin the roller centrifugal-pendulum vibration absorbing device intotranslational motion (sliding motion) along the guide surface that doesnot involve rotation of the roller about the center of gravity androtational motion of the roller about the center of gravity, and treatedmotion of the roller as the total of swing motion of the roller onlyabout the pendulum fulcrum without rotation about the center of gravityand rotational motion of the roller about the center of gravity.

Here, it is known that when the distance from the rotational center RCto the pendulum fulcrum PF is defined as “R” and the distance from thependulum fulcrum PF to the center of gravity G of the mass body isdefined as “r”, the order of vibration of the mass body provided in thecentrifugal-pendulum vibration absorbing device so as to swing about thependulum fulcrum without rotating about the center of gravity isconveniently represented as √(R/r). In contrast, it is known that theorder of vibration of the roller 120 in the roller centrifugal-pendulumvibration absorbing device is conveniently represented as√[(2·R)/(3·r)]. In the studies, the inventors focused on the differencebetween √[(2·R)/(3·r)] and √(R/r) (a decrease). Then, in the light ofthe fact that translational motion of the roller 120 along the guidesurface 111 corresponds to swing motion of the mass body about thependulum fulcrum PF, the inventors estimated that the difference between√[(2·R)/(3·r)] and √(R/r) was caused by rotational motion of the roller120 about the center of gravity G, specifically, the moment of inertiadue to rotation of the roller 120 about the center of gravity G whichwas proportional to the square of the ratio (r/r_(r)) between the radiusr_(r) of the roller 120 and the distance r from the pendulum fulcrum PFto the center of gravity G of the roller 120, and derived the followingformula (10). It should be noted that “n_(r)” in the formula (10)indicates the order of vibration of the roller 120, “m_(r)” indicatesthe mass of the roller 120, “I_(r)” indicates the moment of inertia ofthe roller 120, “m·r²” indicates the moment of inertia due totranslation of the roller 120, and “I_(r)·(r/r_(r))²” indicates themoment of inertia due to rotation of the roller 120. Throughverifications performed by analyses or the like, the inventors confirmedthat the estimation discussed above was extremely adequate, and thatmotion of the mass body provided in the centrifugal-pendulum vibrationabsorbing device and coupled to the support member so as to swing aboutthe pendulum fulcrum and rotate about the center of gravity might betreated as the total of swing motion of the mass body about the pendulumfulcrum without rotation about the center of gravity and rotationalmotion of the mass body about the center of gravity irrespective of theform (structure).

$\begin{matrix}\lbrack {{Formula}\mspace{14mu} 5} \rbrack & \; \\\begin{matrix}{n_{r} = \sqrt{\frac{2R}{3r}}} \\{= \sqrt{\frac{R}{r \cdot ( {1 + \frac{I_{r}}{m_{r} \cdot r_{r}^{2}}} )}}} \\{= \sqrt{\frac{m_{r} \cdot R \cdot r}{{m_{r} \cdot r^{2}} + {I_{r} \cdot ( \frac{r}{r_{r}} )^{2}}}}}\end{matrix} & (10)\end{matrix}$

Meanwhile, a distance d1 along the guide surface 111 from a point oftangency ta between the guide surface 111 and the roller 120 with theroller 120 stationary at the swing center to a point of tangency tbbetween the guide surface 111 and the roller 120 with the roller 120swung to one side in the swing range is represented as d1=(r+r_(r))·φfrom the sum (r+r_(r)) of the distance r from the pendulum fulcrum PF tothe center of gravity G of the roller 120 and the radius r_(r) of theroller 120 and the rotational angle φ of the roller 120 (the center ofgravity G) about the pendulum fulcrum PF. In addition, a distance d2along the outer peripheral surface of the roller 120 from a point oftangency ta between the guide surface 111 and the roller 120 with theroller 120 stationary at the swing center to a point of tangency tbbetween the guide surface 111 and the roller 120 with the roller 120swung to one side in the swing range is represented as d2=r_(r)·(φ+θ)from the sum (φ+θ) of the rotational angle φ of the roller 120 about thependulum fulcrum PF and the rotational angle θ of the roller 120 aboutthe center of gravity G and the radius r_(r) of the roller. Then, if theroller 120 rolls on the guide surface 111 without slipping, the distanced1 and the distance d2 coincide with each other (d1=d2), and therelationship θ/φ=r/r_(r) is met. Thus, by utilizing this relationship,the ratio (r/r_(r)) between the radius r_(r) of the roller 120 and thedistance r from the pendulum fulcrum PF to the center of gravity G ofthe roller 120 can be replaced with the ratio (θ/φ) between therotational angle φ of the roller 120 about the pendulum fulcrum PF andthe rotational angle θ of the roller 120 about the center of gravity.Consequently, the moment of inertia (I_(r)·(r/r_(r))²) due to rotationof the roller 120 about the center of gravity G can be represented asI_(r)·(θ/φ)² using the ratio (θ/φ) between the rotational angle φ of theroller 120 about the pendulum fulcrum PF and the rotational angle θ ofthe roller 120 about the center of gravity.

Thus, the order of vibration of the mass body provided in thecentrifugal-pendulum vibration absorbing device and coupled to thesupport member so as to swing about the pendulum fulcrum and rotateabout the center of gravity can be determined on the basis of the orderof vibration of the mass body which swings about the pendulum fulcrumwithout rotation about the center of gravity and further inconsideration of rotational motion of the mass body about the center ofgravity (the moment of inertia due to rotation), that is, the rotationalangle of the mass body about the pendulum fulcrum and the rotationalangle of the mass body about the center of gravity. Specifically, in thecase where the centrifugal-pendulum vibration absorbing device is notdisposed within the liquid chamber which stores the liquid (in the caseof a dry centrifugal-pendulum vibration absorbing device), and when theorder of vibration is defined as “n_(z)”, the mass of the mass body isdefined as “m”, the distance from the rotational center RC to thependulum fulcrum PF is defined as “R”, the distance from the pendulumfulcrum PF to the center of gravity G of the mass body is defined as“r”, the rotational angle of the mass body about the pendulum fulcrum PFis defined as “φ”, the rotational angle of the mass body about thecenter of gravity G is defined as “θ”, and the moment of inertia of themass body is defined as “I”, the order of vibration n_(z) can bedetermined using the following formula (11):

$\begin{matrix}\lbrack {{Formula}\mspace{14mu} 6} \rbrack & \; \\\begin{matrix}{n_{z} = \sqrt{\frac{m \cdot R \cdot r}{{m \cdot r^{2}} + {I \cdot ( \frac{\theta}{\phi} )^{2}}}}} \\{= \sqrt{\frac{R}{r} \cdot \frac{m \cdot r^{2}}{{m \cdot r^{2}} + {I \cdot ( \frac{\theta}{\phi} )^{2}}}}}\end{matrix} & (11)\end{matrix}$

Further, in determining the order of vibration n of the mass body 12 inthe centrifugal-pendulum vibration absorbing device 10 disposed withinthe fluid transmission chamber 2 (a liquid chamber) which stores theworking oil (a liquid), a force caused by the centrifugal liquidpressure generated in the fluid transmission chamber 2 along withrotation of the driven member 83 serving as a rotary element to act onthe mass body 12 may be considered as with the formula (9) given above.That is, in order to introduce the value a which indicates the forcecaused by the centrifugal liquid pressure to act on the mass body 12into the formula (11), “R/r” on the rightmost side of the formula (11)may be replaced with “(R/r−α)” in consideration of the relationshipbetween a simple formula n=√(R/r) indicating the order of vibration ofthe mass body provided in the centrifugal-pendulum vibration absorbingdevice so as to swing about the pendulum fulcrum without rotating aboutthe center of gravity and the formula (9) given above.

Thus, in the wet centrifugal-pendulum vibration absorbing device 10disposed within the fluid transmission chamber 2 which stores theworking oil, and when the order of vibration is defined as “n”, the massof the mass body 12 is defined as “m”, the distance from the rotationalcenter RC to the pendulum fulcrum PF is defined as “R”, the distancefrom the pendulum fulcrum PF to the center of gravity G of the mass body12 is defined as “r”, the rotational angle of the mass body 12 about thependulum fulcrum PF is defined as “φ”, the rotational angle of the massbody 12 about the center of gravity G is defined as “θ”, the moment ofinertia of the mass body 12 is defined as “I”, and a value obtained bydividing the force Fp caused by the centrifugal hydraulic pressure(centrifugal liquid pressure) to act on the mass body 12 by the squareof the rotational angular speed ω and further dividing the resultingquotient by the product of the mass m and the distance r is defined as“α”, the order of vibration n may be determined using the followingformula (12):

$\begin{matrix}\lbrack {{Formula}\mspace{14mu} 7} \rbrack & \; \\{n = \sqrt{\frac{m \cdot r^{2} \cdot ( {\frac{R}{r} - \alpha} )}{\lbrack {{m \cdot r^{2}} + {I \cdot ( \frac{\theta}{\phi} )^{2}}} \rbrack}}} & (12)\end{matrix}$

When the order of vibration generated by the engine is defined as“Ntag”, the centrifugal-pendulum vibration absorbing device 10 ispreferably designed such that the order of vibration n obtained from theformula (12) given above meets the following relational formula:Ntag−0.2≦n≦Ntag+0.2  (13),more preferably,Ntag−0.1≦n≦Ntag+0.1  (14)

That is, it is possible to adequately set the order of vibration n ofthe mass body 12 in consideration of the effect of the manufacturingtolerance or the like by determining parameters such as the mass m andthe shape (the moment of inertia I) of the mass body 12, the distances Rand r, and the rotational angles θ and φ so as to meet the formula (13)or (14) given above. In the wet centrifugal-pendulum vibration absorbingdevice including the mass body 12 x which swings about the pendulumfulcrum PF without rotating about the center of gravity, parameters suchas the mass m and the shape (the moment of inertia I) of the mass body12, the distances R and r, and the rotational angles θ and φ may bedetermined such that the order of vibration n_(x) obtained from theformula (9) given above meets the formula (13) or (14) given above. Inthe dry centrifugal-pendulum vibration absorbing device including themass body coupled to the support member so as to swing about thependulum fulcrum and rotate about the center of gravity, parameters suchas the mass m and the shape (the moment of inertia I) of the mass body12, the distances R and r, and the rotational angles θ and φ may bedetermined such that the order of vibration n_(z) obtained from theformula (11) given above meets the formula (13) or (14) given above. Thecentrifugal-pendulum vibration absorbing device 10 etc. may be designedsuch that the order of vibration n_(x), n_(z), n obtained from theformula (9), (11), (12), respectively, may perfectly coincide with theorder Ntag of vibration to be damped caused by the engine, or may bedesigned such that the order of vibration n_(x), n_(z), n is includedwithin a narrow range centered on the order Ntag (for example, in arange of Ntag±0.05).

The order Ntag of vibration to be damped by the centrifugal-pendulumvibration absorbing device 10 etc. basically corresponds to the numberof cylinders of the engine to which the centrifugal-pendulum vibrationabsorbing device 10 etc. is coupled, and may be determined as Ntag=1.5for three-cylinder engines and Ntag=2 for four-cylinder engines, forexample. It should be noted, however, that the order Ntag of vibrationto be damped is not limited to the value corresponding to the number ofcylinders of the engine, and may be a value obtained by slightlyincreasing or decreasing the value corresponding to the number ofcylinders of the engine in consideration of the mode of use, thecharacteristics, or the like of the damper mechanism, the lock-upclutch, or the like. In setting the order of vibration in thecentrifugal-pendulum vibration absorbing device 10 etc., further, thevalue obtained from the formula (9), (11), or (12) may be determined asa temporary order, and the temporary order may be increased or decreased(offset) on the basis of the results of a simulation or an experiment orthe like to obtain the final order of vibration.

If the order of vibration n or n_(z) of the mass body 12 in thecentrifugal-pendulum vibration absorbing device 10 etc. including themass body 12 coupled to the support member 11 so as to swing about thependulum fulcrum PF and rotate about the center of gravity G isdetermined on the basis of the order Ntag of vibration generated by theengine serving as the drive device in consideration of at least therotational angle φ of the mass body 12 about the pendulum fulcrum PF andthe rotational angle θ of the mass body 12 about the center of gravity Gas described above, the vibration absorbing performance of thecentrifugal-pendulum vibration absorbing device 10 etc. can be improvedby adequately setting the order of vibration n or n_(z) of the mass body12.

In a starting device of a dry type, for example, a fluid transmissiondevice including a pump impeller, a turbine runner, a stator, and soforth may be omitted, or a mass body that serves as a mass of a dynamicdamper may be separately provided. The rotary element to which thecentrifugal-pendulum vibration absorbing device 10 is coupled is notlimited to the driven member (an output element) of the dampermechanism, and may be the intermediate member or the drive member (aninput element) of the damper mechanism. Alternatively, the rotaryelement may be any rotary member mechanically coupled to the drivedevice to rotate such as a rotary member (a rotary shaft) providedwithin the transmission other than a rotary element forming the dampermechanism. The correspondence between the main elements of theembodiment described above and the main elements of the inventiondescribed in the “SUMMARY OF THE INVENTION” section does not limit theelements of the invention described in the “SUMMARY OF THE INVENTION”section, because the embodiment is an example given for the purpose ofspecifically describing a mode for carrying out the invention describedin the “SUMMARY OF THE INVENTION” section. That is, the embodiment ismerely a specific example of the invention described in the “SUMMARY OFTHE INVENTION” section, and the invention described in the “SUMMARY OFTHE INVENTION” section should be construed on the basis of thedescription in that section.

While an embodiment has been described above, it is a matter of coursethat the present invention is not limited to the embodiment in any way,and that the present invention may be modified in various ways withoutdeparting from the scope and sprit of the present invention.

The present invention can be utilized in the centrifugal-pendulumvibration absorbing device manufacturing industry.

The invention claimed is:
 1. A centrifugal-pendulum vibration absorbingdevice comprising: a support member coupled to a rotary element that isrotated by power from a drive device; and a mass body coupled to thesupport member so as to swing about a pendulum fulcrum and rotate abouta center of gravity, wherein the centrifugal-pendulum vibrationabsorbing device is structured such that an order of vibration of themass body is determined on the basis of an order of vibration generatedby the drive device in consideration of at least a rotational angle ofthe mass body about the pendulum fulcrum and a rotational angle of themass body about the center of gravity.
 2. The centrifugal-pendulumvibration absorbing device according to claim 1, wherein the order ofvibration of the mass body is determined on the basis of the order ofvibration generated by the drive device from a distance from arotational center of the rotary element to the pendulum fulcrum, adistance from the pendulum fulcrum to the center of gravity of the massbody, a mass of the mass body, and a product of a moment of inertia ofthe mass body and a square of a ratio between the rotational angle ofthe mass body about the pendulum fulcrum and the rotational angle of themass body about the center of gravity.
 3. The centrifugal-pendulumvibration absorbing device according to claim 1, wherein the supportmember and the mass body are disposed within a liquid chamber thatstores a liquid, and the order of vibration is determined further inconsideration of a force that acts on the mass body caused by acentrifugal liquid pressure generated within the liquid chamber when thedrive device rotates.
 4. The centrifugal-pendulum vibration absorbingdevice according to claim 3, wherein when the order of vibration isdefined as “n”, a mass of the mass body is defined as “m”, a distancefrom a rotational center to the pendulum fulcrum is defined as “R”, adistance from the pendulum fulcrum to the center of gravity of the massbody is defined as “r”, the rotational angle of the mass body about thependulum fulcrum is defined as “φ”, the rotational angle of the massbody about the center of gravity is defined as “θ”, a moment of inertiaof the mass body is defined as “I”, and a value obtained by dividing theforce caused by the centrifugal liquid pressure by a square of arotational angular speed of the rotary element and further dividing theresulting quotient by a product of the mass of the mass body and thedistance from the pendulum fulcrum to the center of gravity of the massbody is defined as “α”, the order of vibration “n” is determined usingthe following relational formula:n=√{m·r ²·(R/r−α)/[m·r ² +I·(θ/φ))²]}.
 5. The centrifugal-pendulumvibration absorbing device according to claim 1, wherein when the orderof vibration is defined as “n”, a mass of the mass body is defined as“m”, a distance from a rotational center to the pendulum fulcrum isdefined as “R”, a distance from the pendulum fulcrum to the center ofgravity of the mass body is defined as “r”, the rotational angle of themass body about the pendulum fulcrum is defined as “φ”, the rotationalangle of the mass body about the center of gravity is defined as “θ”,and a moment of inertia of the mass body is defined as “I”, the order ofvibration “n” is determined using the following relational formula:n=√{m·R·r/[m·r ² +I·(θ/φ)²]}.
 6. The centrifugal-pendulum vibrationabsorbing device according to claim 5, wherein when the order ofvibration generated by the drive device is defined as “Ntag”, thecentrifugal-pendulum vibration absorbing device is designed to meet thefollowing relational formula:Ntag−0.2≦n≦Ntag+0.2.
 7. An order setting method for acentrifugal-pendulum vibration absorbing device including a supportmember coupled to a rotary element that is rotated by power from a drivedevice and a mass body coupled to the support member so as to swingabout a pendulum fulcrum and rotate about a center of gravity,comprising: determining an order of vibration of the mass body on thebasis of an order of vibration generated by the drive device inconsideration of at least a rotational angle of the mass body about thependulum fulcrum and a rotational angle of the mass body about thecenter of gravity.
 8. The order setting method for acentrifugal-pendulum vibration absorbing device according to claim 7,wherein the order of vibration of the mass body is determined on thebasis of the order of vibration generated by the drive device from adistance from a rotational center of the rotary element to the pendulumfulcrum, a distance from the pendulum fulcrum to the center of gravityof the mass body, a mass of the mass body, and a product of a moment ofinertia of the mass body and a square of a ratio between the rotationalangle of the mass body about the pendulum fulcrum and the rotationalangle of the mass body about the center of gravity.
 9. The order settingmethod for a centrifugal-pendulum vibration absorbing device accordingto claim 7, wherein the support member and the mass body are disposedwithin a liquid chamber that stores a liquid, and the order of vibrationis determined further in consideration of a force that acts on the massbody caused by a centrifugal liquid pressure generated within the liquidchamber when the drive device rotates.
 10. The order setting method fora centrifugal-pendulum vibration absorbing device according to claim 9,wherein when the order of vibration is defined as “n”, a mass of themass body is defined as “m”, a distance from a rotational center to thependulum fulcrum is defined as “R”, a distance from the pendulum fulcrumto the center of gravity of the mass body is defined as “r”, therotational angle of the mass body about the pendulum fulcrum is definedas “φ”, the rotational angle of the mass body about the center ofgravity is defined as “θ”, a moment of inertia of the mass body isdefined as “I”, and a value obtained by dividing the force caused by thecentrifugal liquid pressure by a square of a rotational angular speed ofthe rotary element and further dividing the resulting quotient by aproduct of the mass of the mass body and the distance from the pendulumfulcrum to the center of gravity of the mass body is defined as “α”, theorder of vibration “n” is determined using the following relationalformula:n=√{m·r ²·(R/r−α)/[m·r ² +I·(θ/φ)²]}.
 11. The order setting method for acentrifugal-pendulum vibration absorbing device according to claim 7,wherein when the order of vibration is defined as “n”, a mass of themass body is defined as “m”, a distance from a rotational center to thependulum fulcrum is defined as “R”, a distance from the pendulum fulcrumto the center of gravity of the mass body is defined as “r”, therotational angle of the mass body about the pendulum fulcrum is definedas “φ”, the rotational angle of the mass body about the center ofgravity is defined as “θ”, and a moment of inertia of the mass body isdefined as “I”, the order of vibration “n” is determined using thefollowing relational formula:n=√{m·R·r/[m·r ² +I·(θ/φ)²]}.
 12. The order setting method for acentrifugal-pendulum vibration absorbing device according to claim 11,wherein when the order of vibration generated by the drive device isdefined as “Ntag”, the centrifugal-pendulum vibration absorbing deviceis designed to meet the following relational formula:Ntag−0.2≦n≦Ntag+0.2.